If a man walks to his office at `3/5th` of his original speed. He reaches there 10 minutes late. How much time will he take to reach his office if he walks at his original speed? What is necessary to know the answer of the question?
(A) The distance of his office
(B) His original speed

Options

A. IF I alone is sufficient
B. If II alone is sufficient
C. I and II together are not sufficient
D. Neither I isneeded nor II is neede

Answer

To solve the problem, we can follow these steps:

### Step 1: Define Variables
Let the original speed of the man be \( s \) (in some units, e.g., km/h) and the usual time taken to reach the office be \( t \) (in minutes).

### Step 2: Calculate Distance
The distance to the office can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} = s \times t \]

### Step 3: Determine New Speed
When the man walks at \( \frac{3}{5} \) of his original speed, his new speed becomes:
\[ \text{New Speed} = \frac{3}{5}s \]

### Step 4: Calculate Time Taken at New Speed
When walking at this new speed, the time taken to reach the office is:
\[ \text{New Time} = \frac{\text{Distance}}{\text{New Speed}} = \frac{st}{\frac{3}{5}s} = \frac{5t}{3} \]

### Step 5: Set Up the Equation for Late Arrival
According to the problem, he arrives 10 minutes late when walking at the new speed. Therefore, we can set up the equation:
\[ \frac{5t}{3} = t + 10 \]

### Step 6: Solve the Equation
To solve for \( t \), we first eliminate the fraction by multiplying the entire equation by 3:
\[ 5t = 3t + 30 \]
Now, subtract \( 3t \) from both sides:
\[ 5t - 3t = 30 \implies 2t = 30 \]
Now, divide by 2:
\[ t = 15 \text{ minutes} \]

### Step 7: Calculate Time at Original Speed
Since \( t \) represents the time taken at the original speed, the man will take:
\[ \text{Time at Original Speed} = t = 15 \text{ minutes} \]

### Conclusion
The man will take 15 minutes to reach his office if he walks at his original speed.

### Necessary Information
To answer the question, we need to know:
- (A) The distance of his office
- (B) His original speed

However, in this case, neither the distance nor the original speed is necessary to find the time taken at the original speed, as we derived it solely from the information given about the late arrival.